Lecture
This lecture delves into the derivation of the local kinetic dispersion relation for electrostatic instabilities in inhomogeneous magnetized plasmas, focusing on kinetic effects like wave-particle resonances and finite Larmor radius effects. Topics covered include the interchange instability mechanism, drift waves, and wave-particle interactions. Analytical solutions for Electron Plasma Waves (EPWs) and Ion Acoustic Waves (IAWs) are explored using the resonant approximation method. The lecture also discusses the application of the dispersion relation to study various types of waves and instabilities in magnetized plasmas. Assumed prior knowledge includes the derivation of linear kinetic dispersion relations in homogeneous, unmagnetized plasmas.